JP6856286B1 - BESO topology optimization method based on dynamic evolution rate and adaptive grid - Google Patents

Abstract

PROBLEM TO BE SOLVED: To provide a BESO topology optimization method based on a dynamic evolution rate and an adaptive grid. A finite element model was created for the basic structure to be optimized, design domains, loads, boundary conditions and grid sizes were defined, constraints and parameters required for BESO were determined, and the grid was divided. Perform finite element analysis on the structure, calculate the unit sensitivity under the objective function and the constraint, filter the unit sensitivity, update the undetermined multiplier of the constraint Lagrange, build the sensitivity of the Lagrange function, the current iteration Determine the evolution rate of the current iterative step based on the dynamic evolution rate function of the Logistic function according to the volume factor of the step, and update the design variables based on the set constraint function to set the constraints and convergence conditions. It includes determining whether or not the conditions are met, and if not satisfied, updating the grid adaptively, performing unit updates, and stopping the iteration when the conditions are met. [Selection diagram] Fig. 1

Description

The present invention relates to a technical field of structural topology optimization, specifically, a BESO topology optimization method based on a dynamic evolution rate and an adaptive grid, and an application thereof.

Structural topology optimization is often applied in the field of optimization processing such as architecture and 3D printing. The purpose of topology optimization is to find the optimal topology that meets the design requirements in the design domain of the structure, to maximize the properties of the material, and to ensure that the structure has the highest external resistance efficiency. Among the most commonly used structural optimization design methods, most continuum topology optimization methods, including bidirectional evolutionary structural optimization (BESO), are based on finite element technology, that is, continuums. Is divided into grids and discretized, and then the iterative operation of topology optimization is performed according to the optimization rules. BESO topology optimization is an evolutionary topology optimization technique based on iterative calculations, and each iterative step requires a finite element analysis of the structural form of the current iterative step. Since structural finite element calculation is required and it is necessary to perform finite element structural calculation for the number of optimization iterative steps, calculation time and calculation amount are required.

In one topology-optimized design domain, a single finite element computation is closely related to the grid density, and in the case of a two-dimensional structure, when the grid density per unit length doubles, the entire computation domain. In the case of a three-dimensional structure, if the number of grids in is increased by 4 times and the grid density per unit length is increased by 1 time, the number of grids in the entire calculation domain is increased by 8 times, but theoretically. , It is necessary to subdivide the grid as much as possible so that the optimum design itself is close to a continuum. If the grid is too coarse, the calculation time can be saved, but the calculation accuracy cannot be ensured.

Chinese Patent Application Publication No. 110348102

The present invention discloses a BESO topology optimization method based on the dynamic evolution rate of inverse tangentiality and its application. First, for the basic structure of the topology optimization target, a finite element grid is used under predetermined boundary and load conditions. To discrete the design domain, obtain a finite element model, determine the parameters related to initialization, perform a finite element analysis on the finite element model, and calculate the overall sensitivity of each unit of the finite element model. , The current dynamic evolution rate of the finite element model should be constructed based on the inverse tangential dynamic evolution rate function and updated in the current iterative step of the finite element model based on the current dynamic evolution rate of the finite element model. The number of units is determined, the finite element model is updated and optimized based on the number of units to be updated and the overall sensitivity, and the structure of the current updated finite element model satisfies the constraint condition or convergence condition. Then, the optimization is finished and the optimization model is output. The present invention utilizes the dynamic evolution rate to increase the speed of topology optimization of the basic structure and improve the efficiency and flexibility of topology optimization.

In order to solve the shortcomings and defects of the prior art, the first object of the present invention is to provide a BESO topology optimization method based on the dynamic evolution rate and the adaptive grid, and the present invention employs the adaptive grid technology. By adaptively adjusting the grid density in the topology optimization design process, the amount of calculation for a single finite element analysis can be significantly reduced while ensuring high calculation accuracy, and the Logistic function is used. Therefore, in the early stage of the topology optimization process, the high evolution rate is maintained, the evolution of the topology structure is accelerated, and in the intermediate and final stages of the optimization design, the low evolution rate is ensured to ensure stable convergence of the structure. Automatically switches to, thereby significantly reducing the number of iterative steps required for the entire topology optimization process, as well as significantly reducing the total amount of computation and computation time for the entire continuum topology optimization.

A second object of the present invention is to provide an application of a BESO topology optimization method based on a dynamic evolution rate and an adaptive grid.

A third object of the present invention is to provide a storage medium.

A fourth object of the present invention is to provide a computing device.

In order to achieve the above first object, the present invention
Step S1 to create a finite element model for the basic structure of the topology optimization target and define the design domain, load, boundary conditions and grid size,
Step S2 to determine the constraint value and the parameters required for the BESO method,
In step S3, which performs finite element analysis on the structure in which the grid is divided and calculates the objective function and the unit sensitivity under each constraint condition,
Step S4, which filters the unit sensitivity, updates the undetermined multiplier of the constraint Lagrange, and builds the sensitivity of the Lagrange function,
Step S5, which determines the evolution rate of the current iterative step based on the dynamic evolution function of the Logistic function according to the volume fraction of the current iterative step,
The design variables are updated based on the set constraint function, it is determined whether all the constraints and convergence conditions are satisfied, and if not, the grid is first updated by the adaptive grid method, and then Step S6 to update the unit to
Provided is a BESO topology optimization method based on a dynamic evolution rate and an adaptive grid, including step S7, which repeats steps S3 to S6 to stop the iterative process when constraints and convergence criteria are met.

As a preferred technique, in step S2, the parameters required for the BESO method include a displacement limit, a primary natural frequency limit of the structure, a filtering radius for filtering sensitivity, and a volume ratio limit for topology optimization. ..

As a preferred technique, in step S3, the average compliance of the objective function is minimal.

As a preferred technique, in step S4, the step of filtering the unit sensitivity is specifically
This includes a step in which the final sensitivity of a unit is the weighted average of the sensitivities of all the units within the installation range around the unit according to the distance.

（式中、ＥＲ、ＥＲ_ｍａｘ及びＥＲ_ｍｉｎはそれぞれ最適化対象の現在の進化率、設定された最大進化率及び最小進化率を表し、Ｖ^＊は目的体積分率を表し、Ｖ_ｉは現在の反復ステップの実体ユニットの体積を表す）として表される。 As a preferred technical proposal, in step S5, the evolution rate of the current iterative step is determined based on the dynamic evolution rate function of the Logistic function, and the function based on the dynamic evolution rate of the Logistic function is specifically.

(Wherein, _{ER, ER max} and _{ER min} Current evolution rate to be optimized, respectively, represents the maximum evolution rate and minimum evolution rate set, ^{V *} represents the desired volume fraction, _{V i} is the current Represents the volume of the entity unit of the iterative step).

As a preferred technique, in step S6, the step of updating the grid by the adaptive grid method specifically comprises
Using the fine grid-to-coarse grid adaptive adjustment mode, the design domain of the structure is divided into the finest level grids, and the sensitivity of each unit is calculated based on the objective function and constraints of the topology optimization problem. Check the sensitivity values of the units in the search box sequentially, and if the sensitivity values of the units in a search box are all zero and there are no connection points on all sides of the units in the search box, combine them. It includes the step of making the unit of the previous fineness level and finally combining it as the highest level unit by updating the grid and combining the grid units.

In order to achieve the second object of the present invention, the present invention provides an application of the BESO topology optimization method based on the dynamic evolution rate and the adaptive grid, and the dynamic evolution rate and the adaptive grid described in the first object. Applying the based BESO topology optimization method to the topology optimization of the cantilever structure,
The basic structure of step S1 is the basic structure of the object to be optimized for the cantilever by performing topology optimization.
When steps S1 to S7 are executed, a cantilever optimized structure is obtained.

In order to achieve the third object of the present invention, the present invention is a storage medium in which a program is stored, and when the program is executed by a processor, the dynamic evolution rate and the dynamic evolution rate described in the first object are achieved. Provided is a storage medium that realizes a BESO topology optimization method based on an adaptive grid.

In order to achieve the fourth object of the present invention, the present invention is a computing device including a processor and a memory for storing a processor-executable program.
When the processor executes a program stored in a memory, it provides a computing device that realizes a BESO topology optimization method based on the dynamic evolution rate and the adaptive grid described in the first purpose.

Compared with the prior art, the present invention has the following advantages and beneficial effects.
(1) In the present invention, by adopting adaptive grid technology and adaptively adjusting the grid density in the topology optimization design process, the amount of calculation for a single finite element analysis can be reduced while ensuring high calculation accuracy. Significantly reduce.
(2) In the present invention, based on the dynamic evolution rate function Logistic function, in the initial stage of topology optimization process, maintaining a high evolution rate, accelerate the evolution of topology structure, and intermediate stages of optimized design In the final stage, it automatically switches to a lower evolution rate to ensure stable convergence of the structure, which significantly reduces the number of iterative steps required for the entire topology optimization process, as well as continuum topology optimization. Significantly reduce the total amount of calculation and calculation time.

It is a flowchart of the BESO method based on the adaptation grid of this embodiment. It is a schematic diagram of the quadtree structure of this Example. It is a schematic diagram of the sensitivity value check of the adjustment search process of the adaptive grid of this embodiment. It is a schematic diagram of the grid unit combination of the adjustment search process of the adaptive grid of this embodiment. It is a schematic diagram of the whole process of the adjustment operation of the adaptation grid of this embodiment. It is a schematic diagram of the initial design domain of the 2D short cantilever beam structure of this embodiment. It is a schematic diagram of the optimum topology of the case 2 of the cantilever beam of this Example.

In order to clarify the object, technical proposal, and advantage of the present invention, the present invention will be described in more detail below with reference to the drawings and examples. It should be noted that the specific examples described here are merely for interpreting the present invention and do not limit the present invention.

Example As shown in FIG. 1, the present embodiment provides a BESO topology optimization method based on the dynamic evolution rate and the adaptive grid, which method comprises steps S1 to S7.
Step S1: For the basic structure of the topology optimization target, a finite element model is created, and the design domain, load, boundary conditions, and grid size are defined.
Step S2: Constraint values and other parameters required for the BESO method, such as displacement limit value d ^* , structure primary natural frequency limit value ω ^* , filtering radius r _min for filtering sensitivity, topology optimized volume ratio. Determine the limit value V ^{*, etc.}
The displacement limit value d ^* is generally an upper limit value, that is, the displacement d at a specific point of the structure under force ^{is required to be d *} or less, and is the primary natural frequency of the structure. The limit value ω ^* may be an upper limit value or a lower limit value. After directly calculating the sensitivity of a unit, the sensitivity finally used is obtained by weighted averaging the sensitivity of units within a predetermined range around it according to the magnitude of the distance, and filters the sensitivity. The filtering radius r _min for this is what determines this range, and the topology-optimized volume ratio limit value V ^* is the ratio of the volume of the structure after topology optimization to the volume of the entire design domain.
Step S3: A finite element analysis is performed on the structure in which the grid is divided, and the sensitivity of each unit under the objective function and each constraint, that is, the displacement sensitivity, the frequency sensitivity, and the like are calculated.
In this embodiment, according to the processing method using the BESO method, the average compliance of the objective function is the minimum.
Step S4: Filter the unit sensitivity, update the undetermined multiplier of the constraint Lagrange, and build the sensitivity of the Lagrange function.
The unit sensitivity is filtered, and the weighted average of the sensitivities of all the units within a predetermined range around a certain unit according to the distance is used as the final sensitivity of the unit. The closer the distance, the larger the weighted value.
Step S5: The evolution rate of the current iterative step is determined according to the volume fraction of the current iterative step, and here, it is performed based on the dynamic evolution rate function of the Logistic function, that is, as in Eq. (1-2). Become.
Step S6: The design variable is updated based on the preset constraint function, it is determined whether or not all the constraints and convergence conditions are satisfied, and if not, the grid is first updated (adaptive grid). Method), then update the unit.
Step S7: When steps S3 to S6 are repeated and each constraint condition and convergence criterion are satisfied, the iterative process is stopped.

As shown in FIG. 2, in this embodiment, a method of realizing an adaptive grid is described by taking a two-dimensional problem as an example, and here, three levels of Level 0, Level 1, and Level 2 from coarse to fine. Explaining only the grid of, the classic quadtree is divided from top to bottom into three levels, Level 0, Level 1 and Level 2, and the difference in numbers between the two adjacent levels is quadrupled. is there. Assuming that the smallest square is the basic grid, the Level 2 level unit contains 1x1 basic grids called leaf units, and the Level 1 level unit contains 2x2 basic grids, that is, 2x2. The Level 1 level unit is called a subtree unit, and the Level 0 level unit contains 4x4 basic grids, that is, 2x2 subtree units, and this Level 0 level unit. Is called the root unit.

As shown in FIGS. 3a, 3b and 4, in this embodiment, the BESO method based on the dynamic evolution rate and the adaptive grid produces a quadtree grid and grid adaptation adjustment from a fine grid to a coarse grid. The method of using the mode is explained, that is, first, the design domain of the structure is (n × 2 ^L ) × (m × 2 ^L ) (where L indicates the level of the grid to be adaptively adjusted this time, and the current level is When it is 2, n and m represent the number of grids in the two-dimensional plane of the design domain when dividing the coarse grid, respectively. “The two dimensions of the design domain when the grid level is Level 0, that is, L = 0. The number of grids in the plane ”) is divided into the thinnest level (Level 2) grids containing 3 units, and then according to the principles of the BESO method, based on the objective function and constraints of the topology optimization problem, of each unit. The sensitivity is calculated and the sensitivity values of the four units within each search box (the search box is square, contains four Level 2 level units, and the search boxes do not overlap each other) are calculated according to the method shown in FIG. 3a. , Check in a particular order, and if the sensitivity values of all four units in a search box are zero and there are no connection points on the sides of the units in the search box, combine (coarse) them. One Level 1 level unit. Finally, based on the above steps, the grid units are further coupled (coarse) into Level 0 level units, and the adaptive grid adjustment operation is performed according to the method described above.

式中、Ｖは最適化プロセスにおける構造の体積分率、つまり現在の反復ステップの実体ユニットの体積と設計ドメイン全体の体積との比であり、Ｖ^＊は目的体積分率、即ち、トポロジー最適化設計になった後の実体体積と元の設計ドメインの実体体積との比であり、ＥＲは最適化プロセスにおける進化率であり、ＥＲ_ｍｉｎ及びＥＲ_ｍａｘはそれぞれ所定の最小進化率及び最大進化率である。式（１−１）から明らかなように、最適化の初期に構造の体積分率が１であり、このとき

であり、反復が進むにつれて進化率が減少し、構造の体積分率が目的体積分率まで減少したとき（即ちＶ＝Ｖ^＊）、進化率ＥＲはほぼ最小進化率ＥＲ_ｍｉｎに等しい。 In the initial stage of optimization, the volume fraction of the structure is 1, and at this time, there are many low-sensitivity units in the design domain, and in this case, the calculation efficiency is improved with a larger evolution rate, that is, optimization. As the process progresses, units that have a small effect on the performance of the structure are gradually removed from the structure, and the rest are basically units that have a large effect on the structural performance, and the improvement gradually decreases as the volume fraction decreases. In this way, it is avoided that in the later stages of optimization, an excessive amount of sensitive units are removed at one time, making it difficult to obtain the best results. As can be seen from the above analysis, in the dynamic evolution rate method, there is a certain relationship between the evolution rate and the volume fraction of the structure. Such a relationship is shown as follows.

In the equation, V is the volume fraction of the structure in the optimization process, that is, the ratio of the volume of the body unit of the current iterative step to the volume of the entire design domain, and V ^* is the volume fraction of the object, that is, topology optimization. It is the ratio of the volume fraction after designing to the volume fraction of the original design domain, ER is the volume fraction in the optimization process, and ER _min and ER _max are the predetermined minimum and maximum volume fractions, respectively. is there. As is clear from equation (1-1), the volume fraction of the structure is 1 at the initial stage of optimization, and at this time

When the evolution rate decreases as the iteration progresses and the volume fraction of the structure decreases to the target volume fraction (that is, V = V ^* ), the evolution rate ER is approximately equal to the _{minimum volume fraction ER min.}

式中、ＥＲ、ＥＲ_ｍａｘ及びＥＲ_ｍｉｎはそれぞれ最適化の現在の進化率、設定された最大進化率及び最小進化率であり、Ｖ_ｉは現在の反復ステップの実体ユニットの体積である。 As can be seen from the above analysis, the evolution rate of each iterative step of the dynamic evolution rate method is related to the volume fraction of the structure, according to the relationship between the variable deletion rate and the volume fraction of the structure in the optimization process. In combination with equation (1-1), a mathematical model based on the dynamic evolution rate of the following Structural function is constructed.

Wherein, ER, ER _max and ER _min Current evolution rate optimization, respectively, the maximum evolution rate and minimum evolution rate set, V _i is the volume of the entity unit of the current iteration step.

As explained above, the adaptive grid method and the BESO method based on the dynamic evolution rate are combined to achieve a faster and more efficient improved BESO method (abbreviated as DER-SAM BESO, and the full name is Dynamic Evolution Rate-Self Adaptive Process BESO. The method) is being developed, and the main feature of this improved method is the ability to adaptively adjust the grid density of the design area throughout the optimization process.

In this embodiment, an application of the BESO topology optimization method based on the dynamic evolution rate and the adaptive grid is also provided. Specifically, as shown in FIG. 5, the BESO topology based on the dynamic evolution rate and the adaptive grid described above is also provided. The optimization method is applied to the topology optimization of the planar cantilever beam structure. Taking a 50 mm (height) x 80 mm (width) planar cantilever beam as an example, there is a fixed constraint on the left side and at the midpoint on the right side. There are concentrated load of 9 kN, the performance of the material has a Young's modulus ^{E =} 10 6 MPa, Poisson's ratio [nu = 0.3, the mass density ρ = 1000kg / ^{m 3.} Its adaptive grid method uses three levels of unit size, the difference in area between adjacent level units is four times, and the size of the smallest unit and the units in the uniform grid are the same (uniform grid). The calculation result and the calculation time are used as a comparison of the methods of this embodiment), both of which are (1/100) × (1/64). The two-dimensional cantilever structure of this embodiment is a common structure in mechanical engineering and civil engineering, and the design of the rod structure can be made more rational through topology optimization, which is mainly the use of structural materials. When the amount is constant, the performance of the structural material is fully utilized and the resistance to external force is high, that is, the structure has the best external force resistance for the same material consumption, and the natural frequency is within a certain limiting range. It is reflected by satisfying the constraint conditions such as.

In this embodiment, the feasibility of the method of the present invention is verified by comparing the optimization results for the calculation examples of the optimization methods (including the method of the present invention) under each work constraint condition.
Table 1 shows the cases of three different constraints considered in topology optimization, where d ₁ and ω ₁ show the displacement at the midpoint on the right and the fundamental frequency of the structure. ..

As is clear from the above table, the optimization results of all three different methods can meet the requirements of different work constraints. It also shows that the method of the present invention has good adaptability to each work constraint.

In this embodiment, as shown in FIG. 6, a typical working condition 2 is selected from the above three working conditions, and the optimum topology structure and the convergence curve obtained by three different methods are observed. After that,
(1) different ways resulting topology structure has Naru good similarity.
(2) Both SAM with a constant evolution rate and BESO with a constant evolution rate have undergone more than 70 iterative steps before the entire optimization process converges, whereas DER-SAM based on the Logistics function. BESO takes only 24 iterative steps to converge. It is shown that the dynamic evolution rate of the Logistic function can reduce the iterative step of topology optimization in this calculation example by about 60%.

Hereinafter, the superiority of the present invention in terms of calculation efficiency will be explained by comparing the calculation times of the uniform grid and the adaptive grid, and Table 2 below shows the average simple over the calculation processes of the three methods. The calculation time required for the finite element analysis and the single sensitivity analysis is shown.

Table 2 above shows a comparison of the average solution time and sensitivity average calculation time of computer finite elements by two different grid processing methods, adaptive grid and uniform grid, see average time in uniform grid state. And. Of these, the average solution time of finite elements by the BESO optimization method improved by the adaptive grid method is about 36.7% of the time in the case of a uniform grid, and the average calculation time for calculating the sensitivity is It takes about 52.1% of the time for a uniform grid, which shows that the quadtree-based adaptive grid method is more reliable and more efficient than a conventional uniform grid. It was.

In this example, Table 3 below (total number of units and degrees of freedom in each iterative step) illustrates the effect of the adaptive grid and presents three different constraint cases considered in topology optimization.

The quadtree-based adaptive grid method is optimal, as evidenced by the results of comparing the number of units and degrees of freedom in steps 1, 10, and the last step optimized by each of the improvements described in the table above. By continuously adjusting the level of grid fineness during the optimization process, the scale of the computation for the program to solve the number of units and degrees of freedom is reduced. As you can see from this, in the initial stage, the number of units and the scale of the calculation for solving the degrees of freedom are almost the same for both, but as the program continues to run, the adaptive grid method is finer. When the level of is continuously adjusted and step 10 is reached, the difference between the adaptive grid and the uniform grid becomes very clear. This difference becomes even larger in the late optimization, and in the case of the adaptive grid, the scale of the calculation for the program to solve the number of units and the degrees of freedom is much smaller than the scale of the calculation of the uniform grid. The above data further show that the BESO method improved by adaptive grid technology shows excellent effect on 2D problems and saves 35% of calculation time. Adaptive grid technology can automatically adjust the size of the grid as needed during the optimization process, which adequately solves the computational scale and efficiency challenges for optimization.

As shown in Table 4 below, this table also shows a comparison of the method of the present invention with other methods using dynamic evolution rates and adaptive grids.

As can be seen from Table 4 above, the total time required when using the method of the present invention (DER-SAM BESO based on the Logistic function) is only 22.6% of that of the conventional BESO method, and the calculation efficiency is high. Is greatly improved.

The present embodiment further discloses a storage medium in which a program is stored and when the program is executed by a processor, a BESO topology optimization method based on a dynamic evolution rate and an adaptive grid is further disclosed, and the BESO topology optimization is performed. Specifically, the conversion method is as follows.
Step S1: For the basic structure of the topology optimization target, a finite element model is created, and the design domain, load, boundary conditions, and grid size are defined.
Step S2: Constraint values and other parameters required for the BESO method, such as displacement limit value d ^* , structure primary natural frequency limit value ω ^* , filtering radius r _min for filtering sensitivity, topology optimized volume ratio. Determine the limit value V ^{*, etc.}
The displacement limit value d ^* is generally an upper limit value, that is, the displacement d at a specific point of the structure under force ^{is required to be d *} or less, and is the primary natural frequency of the structure. The limit value ω ^* may be an upper limit value or a lower limit value. After directly calculating the sensitivity of a unit, the sensitivity finally used is obtained by weighted averaging the sensitivity of units within a predetermined range around it according to the magnitude of the distance, and filters the sensitivity. The filtering radius r _min for this is what determines this range, and the topology-optimized volume ratio limit value V ^* is the ratio of the volume of the structure after topology optimization to the volume of the entire design domain.
Step S3: A finite element analysis is performed on the structure in which the grid is divided, and the sensitivity of each unit under the objective function and each constraint, that is, the displacement sensitivity, the frequency sensitivity, and the like are calculated.
In this embodiment, according to the processing method using the BESO method, the average compliance of the objective function is the minimum.
Step S4: Filter the unit sensitivity, update the undetermined multiplier of the constraint Lagrange, and build the sensitivity of the Lagrange function.
The unit sensitivity is filtered, and the weighted average of the sensitivities of all the units within a predetermined range around a certain unit according to the distance is used as the final sensitivity of the unit. The closer the distance, the larger the weighted value.
Step S5: The evolution rate of the current iterative step is determined based on the dynamic evolution rate function of the Logistic function according to the volume fraction of the current iterative step.
Step S6: The design variable is updated based on the preset constraint function, it is determined whether or not all the constraints and convergence conditions are satisfied, and if not, the grid is first updated (adaptive grid). Method), then update the unit.
Step S7: When steps S3 to S6 are repeated and each constraint condition and convergence criterion are satisfied, the iterative process is stopped.

This embodiment can be applied to the optimization of the cantilever structure, and the optimized cantilever structure can be obtained by the processor performing the procedure of the BESO topology optimization method based on the dynamic evolution rate and the adaptive grid as described above. Be done.

The storage medium in this embodiment may be a medium such as a magnetic disk, an optical disk, a computer memory, a read-only memory (ROM, Read-Only Memory), a random access memory (RAM, Random Access Memory), a U disk, or a mobile hard disk. ..

This embodiment includes a processor and a memory for storing a processor-executable program, and when the processor executes the program stored in the memory, a BESO topology optimization method based on a dynamic evolution rate and an adaptive grid is performed. The BESO topology optimization method, which further discloses the computing device to be realized, is specifically as follows.
Step S1: For the basic structure of the topology optimization target, a finite element model is created, and the design domain, load, boundary conditions, and grid size are defined.
Step S2: Constraint values and other parameters required for the BESO method, such as displacement limit value d ^* , structure primary natural frequency limit value ω ^* , filtering radius r _min for filtering sensitivity, topology optimized volume ratio. Determine the limit value V ^{*, etc.}
The displacement limit value d ^* is generally an upper limit value, that is, the displacement d at a specific point of the structure under force ^{is required to be d *} or less, and is the primary natural frequency of the structure. The limit value ω ^* may be an upper limit value or a lower limit value. After directly calculating the sensitivity of a unit, the sensitivity finally used is obtained by weighted averaging the sensitivity of units within a predetermined range around it according to the magnitude of the distance, and filters the sensitivity. The filtering radius r _min for this is what determines this range, and the topology-optimized volume ratio limit value V ^* is the ratio of the volume of the structure after topology optimization to the volume of the entire design domain.
Step S3: A finite element analysis is performed on the structure in which the grid is divided, and the sensitivity of each unit under the objective function and each constraint, that is, the displacement sensitivity, the frequency sensitivity, and the like are calculated.
In this embodiment, according to the processing method using the BESO method, the average compliance of the objective function is the minimum.
Step S4: Filter the unit sensitivity, update the undetermined multiplier of the constraint Lagrange, and build the sensitivity of the Lagrange function.
The unit sensitivity is filtered, and the weighted average of the sensitivities of all the units within a predetermined range around a certain unit according to the distance is used as the final sensitivity of the unit. The closer the distance, the larger the weighted value.
Step S5: The evolution rate of the current iterative step is determined based on the dynamic evolution rate function of the Logistic function according to the volume fraction of the current iterative step.
Step S6: The design variable is updated based on the preset constraint function, it is determined whether or not all the constraints and convergence conditions are satisfied, and if not, the grid is first updated (adaptive grid). Method), then update the unit.
Step S7: When steps S3 to S6 are repeated and each constraint condition and convergence criterion are satisfied, the iterative process is stopped.

In this embodiment, APDL programming can be performed using the ANSYS software of the computing device, and the finite element analysis platform is an ANSYS that implements a BESO topology optimization method based on dynamic evolution rates and adaptive grids.

This embodiment can be applied to the optimization of the cantilever structure, and is optimized when the processor of the computing device executes the program of the BESO topology optimization method based on the dynamic evolution rate and the adaptive grid stored in the memory. A cantilever structure can be obtained.

The computing device in this embodiment may be a desktop computer, a notebook computer, a smartphone, a PDA handheld terminal, a tablet computer, or another terminal device having a processor function.

The above embodiment is a preferred embodiment of the present invention, but the embodiment of the present invention is not limited by the above embodiment and is made without departing from the spirit and principle of the present invention. , Combinations and simplifications are all equivalent substitution methods and are all within the scope of the invention.

Claims (9)

A BESO topology optimization method based on dynamic evolution rate and adaptive grid.
Step S1 to create a finite element model for the basic structure of the topology optimization target and define the design domain, load, boundary conditions and grid size,
Step S2 to determine the constraint value and the parameters required for the BESO method,
In step S3, which performs finite element analysis on the structure in which the grid is divided and calculates the unit sensitivity under the objective function and constraints,
Step S4, which filters the unit sensitivity, updates the undetermined multiplier of the constraint Lagrange, and builds the sensitivity of the Lagrange function,
Step S5, which determines the evolution rate of the current iterative step based on the dynamic evolution function of the Logistic function according to the volume fraction of the current iterative step,
The design variables are updated based on the set constraint function, it is determined whether all the constraints and convergence conditions are satisfied, and if not, the grid is first updated by the adaptive grid method, and then Step S6 to update the unit to
A BESO topology optimization method comprising steps S3 to S6 to stop an iterative process when constraints and convergence criteria are met. In step S2, the parameters required for the BESO method include a displacement limit value, a primary natural frequency limit value of the structure, a filtering radius for filtering sensitivity, and a volume ratio limit value of topology optimization. The BESO topology optimization method based on the dynamic evolution rate and the adaptive grid according to claim 1. The BESO topology optimization method based on the dynamic evolution rate and the adaptive grid according to claim 1, wherein in step S3, the average compliance of the objective function is the minimum. In step S4, the step of filtering the unit sensitivity is specifically described as
The dynamic evolution according to claim 1, further comprising a step of determining the final sensitivity of the unit by weighted averaging the sensitivities of all the units within the installation range around the unit according to the distance. BESO topology optimization method based on rate and adaptive grid. In step S5, the evolution rate of the current iterative step is determined based on the dynamic evolution rate function of the Logistic function, and the function based on the dynamic evolution rate of the Logistic function is specifically.

(In the equation, ER, ERmax and ERmin represent the current evolution rate of the optimization target, the set maximum evolution rate and the minimum evolution rate, respectively, V * represents the target volume fraction, and Vi represents the current iterative step. The BESO topology optimization method based on the dynamic evolution rate and the adaptive grid according to claim 1, wherein the volume is represented as (representing the volume of an entity unit). In step S6, the step of updating the grid by the adaptive grid method is specifically described as
Using the fine grid-to-coarse grid adaptation mode, the design domain of the structure is divided into the finest level grids, and the sensitivity of each unit is calculated based on the objective function and constraints of the topology optimization problem. Check the sensitivity values of the units in the search box sequentially, and if the sensitivity values of the units in a search box are all zero and there are no connection points on all sides of the units in the search box, combine them. The dynamic evolution rate according to claim 1, further comprising a step of making the unit of the previous fineness level and finally combining it as the highest level unit by performing grid update and grid unit combination. And a BESO topology optimization method based on the adaptive grid. A system for use BESO topology optimization how based on dynamic evolution rate and adaptive grid, BESO topology optimization method based on the dynamic evolution rate and adaptive grid according to any one of claims 1 to 6 Is applied to the topology optimization of the cantilever structure,
The basic structure of step S1 is the basic structure of the object to be optimized for the cantilever by performing topology optimization.
A BESO topology optimization system that obtains a cantilever optimization structure when steps S1 to S7 are executed. A storage medium in which a program is stored
A storage medium, characterized in that, when the program is executed by a processor, the BESO topology optimization method based on the dynamic evolution rate and the adaptive grid according to any one of claims 1 to 6 is realized. A computing device that has a processor and memory for storing a processor-executable program.
When the processor executes a program stored in a memory, the BESO topology optimization method based on the dynamic evolution rate and the adaptive grid according to any one of claims 1 to 6 is realized. Computing equipment.

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